Flying In:
You can fly in to Burlington (BTV) which will put you within minutes of downtown and Shelburne. If you prefer to fly in to a larger airport your options could be Manchester, NH (2 hours), Boston (3.5 hours), or Hartford, CT (4 hours). 

Places to Stay: 

Depending on what you are looking for, I will suggest a few places. 

Heart of the Village Inn Shelburne VT Prices 150-230/night
Book online: 

Inn at Shelburne Farms Shelburne, VT Prices 155-480/night
Phone: 802.985.8498

If you want to stay where there is nightlife and restaurants, you may choose to stay in Burlington especially on the waterfront. All of these locations are within walking distance of downtown Burlington and you may also find them on travelocity or any other site to book. 

Hilton 1 (888) 370 0980
Hotel Vermont 802) 651-0080

B&Bs in Burlington
Lang House (802) 652-2500
Willard Street Inn (800) 577-8712

Other Choices outside of downtown: 

Holiday Inn South Burlington, VT

Holiday Inn Express South Burlington, VT